This invention relates generally to the formation of signals having desired statistical characteristics and more particularly to a design for an integrated circuit chip to produce signals using an autoregressive model.
In various situations, it is desirable to produce an electrical signal or set of electrical signals having a particular frequency spectrum. One technique for producing signals with a desired spectrum is to use what is called an autoregressive model. With this technique, the signal is described in terms of autoregressive coefficients.
To produce a sample of the desired signal, the autoregressive coefficients are combined in a known fashion. The combination of these coefficients is described by an equation: ##EQU1## where
y(N) is the Nth, and current, sample of the generated signal;
q is an index of summation;
y(N-q) is a sample of the generated signal generated q samples before the current sample (for values of (N-q) less than zero, y(N-q) is defined to be zero);
a.sub.q is the qth autoregressive coefficient characterizing the desired signal;
b is a constant also determined as part of the calculation of autoregressive coefficients;
X(N) is the Nth sample of a function representing zero mean white noise with a unit variance; and
M is a constant representing the order of the autoregressive model.
The order of the autoregressive model, M, dictates how closely the spectrum of the generated signal approximates the desired spectrum. The higher the value of M, the closer the approximation. It should be noted, however, that the higher the value of M, the more autoregressive coefficients are required to evaluate Eq. 1. Since the signal is generated by some form of electronic circuitry, more coefficients generally require larger or more complicated circuitry.
The circuitry used to form the signal is called an "autoregressive model simulator". It is desirable for an autoregressive model simulator to be easily constructed, regardless of the order of the model. In some applications, it is desirable to generate several signals simultaneously. Thus, it would be desirable to have circuitry that could generate a plurality of signals.